Don't worry about the tenders in Belize. They use shore side high speed tenders that are a good part of the Belize experience. There is no snorkeling in or around Belize City so you have to make your way out to the outer islands and reefs.
Your ship should offer a shore excursion that picks you up right at the ship for snorkeling, but if you want to go independently here is a link to one option.
Have a great day in Belize!